建置延伸有限元素法分析基材裂縫在一薄膜/基材系統

Implementation of Extended Finite Element Method for a Substrate Crack in a Film/Substrate System

陳俊逸(Jyun-Yi Chen)

指導教授 ： 余念一

元智大學/工程學院/機械工程學系/碩士(2009年)

摘要

延伸有限元素法是由傳統的有限元素法的觀念下所延伸出來。在處理裂縫問題時，每當裂縫發生成長或變化時，傳統有限元素法必須重新去沿著裂縫軌跡作網格。然而延伸有限元素法則不必去重新定義裂縫軌跡以及重新網格化。
本篇論文將討論單邊裂縫的平板受到拉伸或彎矩後，位移與應力場的變化，求出應力強度因子，並且將結果與破壞力學的理論數值作對照。接著討論一基材裂縫在薄膜/基材承受彎矩之後，討論當基材與薄膜不同材料性質時產生的效應，以及裂縫與薄膜/基材界面之間不同的距離的效應，並將其結果與理論值作比較。

關鍵字

延伸有限元素法 ； 裂縫 ； 薄膜

並列摘要

The extended finite element method (X-FEM) is originated from the classical finite element method. Consider crack or discontinuity problems. If the crack grows, one must remesh the finite element model along the crack propagation path in the classical finite element method. However, remeshing is not required for X-FEM even if the crack grows.

The present work studies (1) a plate containing a single edge crack subjected to uniaxial tension, (2) a plate containing a single edge crack subjected to bending moments, and (3) a substrate crack in a thin film/substrate crack subjected to bending moments. The stress intensity factors together with deformation and stress fields in the cracked bodies are computed using X-FEM and are benchmarked with those obtained by fracture mechanics and elasticity theories. The effects of material mismatch and crack location on the stress intensity factor of film/substrate system are also studied.

並列關鍵字

XFEM ； crack ； film

參考文獻

Asadpoure A., Mohammadi S., and Vafai A. (2006a) “Crack analysis in orthotropic media using the extended finite element method,” Thin-Walled Structures, 44, pp. 1031-1038.

Asadpoure A., Mohammadi S., and Vafai A. (2006b) “Modeling crack in orthotopic media using a coupled finite element and partition of unity methods,” Finite Elements in Analysis and Design, 42, pp. 1165-1175.

Belytschko T. and Black T. (1999) “Elastic crack growth in finite elements with minimal remeshing,” International Journal for Numerical Methods in Engineering, 45, pp. 601-620.

Daux C., Moes N., Dolbow J., Sukumar N., and Belytschko T. (2000) “Arbitrary branched and intersecting cracks with the extended finite element method,” International Journal for Numerical Methods in Engineering, 48, pp. 1741-1760.

Dundurs, M.R. (1969). “Edge-bonded dissimilar orthogonal elastic wedges,” Journal of Applied Mechanics, 36, pp. 650–652.